:: deftheorem Def8 defines Integral2 MESFUN12:def 8 :
for X1, X2 being non empty set
for S2 being SigmaField of X2
for M2 being sigma_Measure of S2
for f being PartFunc of [:X1,X2:],ExtREAL
for b₆ being Function of X1,ExtREAL holds
( b₆ = Integral2 (M2,f) iff for x being Element of X1 holds b₆ . x = Integral (M2,(ProjPMap1 (f,x))) );